Coisotropic submanifolds and dual pairs
Symplectic Geometry
2020-02-03 v2 Mathematical Physics
Differential Geometry
math.MP
Abstract
The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and that the corresponding reduced phase space is a (possibly singular) dual pair between the reduced spaces of the given two coisotropic submanifolds. In addition the generalization to a more general tensor field is considered and it is shown that the theory produces Lagrangian evolution relations if and only if the tensor field is Poisson.
Keywords
Cite
@article{arxiv.1306.3249,
title = {Coisotropic submanifolds and dual pairs},
author = {Alberto S. Cattaneo},
journal= {arXiv preprint arXiv:1306.3249},
year = {2020}
}
Comments
29 pages; minor corrections; to appear in Lett. Math. Phys